Q: i bought new iphone 6s plus and i did not set it up, i just opened the phoned and charged it, but after a while it shut down by itself, is this normal or i have a problem with my phone ?

You would need to activate the phone. There is nothing the phone can do without being activated.

If the iPhone is on, the battery will discharge no matter if you are using it or not.

It's very important to follow the setup instructions to avoid problems later on.

Get started with iPhone, iPad, and iPod touch - Apple Support

I believe if you power it up and do not activate it, it will power itself down since there is nothing that you can do with it in that condition. Probably somewhat of a battery saving measure. Until you activate it, you cannot do anything with it, so there is no need for it to be powered on.

This isn't a problem it is just a way to save battery on your phone

Hope this helped!